A cohomological characterisation of Yu's property A for metric spaces (Q422824)

There are various cohomology theories for discrete metric spaces and groups, and the paper under review presents a unifying framework for these, which generalizes group cohomology, Roe's coarse cohomology, Gersten's \(\ell^\infty\)-cohomology and Johnson's bounded cohomology. The authors use this framework to construct a new cohomology theory which yields a cohomological characterization of Yu's property~A, just as Johnson's cohomology gives a characterization of amenability.